Bibliothèque de L'IMIST/CNRST

Includes bibliographical references and index.

Cover13; -- General Systems Theory: Mathematical Foundations -- Copyright Page -- Contents -- Preface -- Chapter I. Introduction -- 1. General Systems Theory: What Is It and What Is It for? -- 2. Formalization Approach for the Development of the Mathematical Theory of General Systems -- Chapter II. Basic Concepts -- 1. Set-Theoretic Concept of a General System -- 2. General Time and Dynamical Systems -- 3. Auxiliary Functions and Some Basic Classification of Systems -- 4. Causality -- Chapter III. General Realization Theory -- 1. Realizability and Dynamical Representation -- 2. Canonical Representation (Decomposition) of Dynamical Systems and Characterization of States -- 3. Constructive Origin of State-Space Representation -- Chapter IV. Linearity -- 1. Linear Time Systems -- 2. Decomposition of Systems Response: State- and Input-Response Functions -- 3. Realization Theory -- 4. Construction of the State Space for a Linear System -- Chapter V. Past-Determinacy -- 1. On the Class of Past-Determined Systems -- 2. State-Space Representation -- 3. Characterization of Past-Determined Systems -- Chapter VI. Stationarity and Time Invariance -- 1. State-Space Stationarity and Time Invariance -- 2. Realization Theory of Time-Invariant Systems -- 3. Stationary Past-Determined Systems -- 4. Axiomatic Construction of a Class of Dynamical Systems -- 5. Abstract Transfer Function -- Chapter VII. Controllability -- 1. Basic Concepts -- 2. Some General Conditions for Controllability -- 3. Controllability of Time Systems -- 4. Overview of Some Basic Linear Time Systems Properties Related to Controllability -- Chapter VIII. Minimal Realization -- 1. Concepts of Minimal Realizations -- 2. Characterization of the Minimal Realization of Stationary Systems -- 3. Uniqueness of Minimal Input-Response Realization -- Chapter IX. Stability -- 1. General Concept of Stability -- 2. Stability of Sets for General Systems -- Chapter X. Interconnections of Subsystems, Decomposition, and Decoupling -- 1. Connecting Operators -- 2. Subsystems, Components, and Decomposition -- 3. Feedback Connection of Components -- 4. Decoupling and Functional Controllability -- 5. Abstract Pole Assignability -- 6. Simplification through Decomposition of Discrete-Time Dynamical Systems -- Chapter XI. Computability, Consistency, and Completeness -- 1. Computation as Dynamical Process -- 2. Fundamental Diagonalization (Goedel) Theorem -- 3. Application of the Fundamental Theorem to Formal Systems -- 4. Realization by Turing Machines -- Chapter XII. Categories of Systems and Associated Functors -- 1. Formation of Categories of General Systems and Homomorphic Models -- 2. Categories of General Systems -- 3. Categories of Time Systems -- 4. Categories of Dynamical Systems -- Appendix I. References and Historical Account -- Appendix II. Alternative Basis for Mathematical General Systems Theory -- 1. Axiomatic Logic Structures -- 2. Topological. Functional Analysis, and Quantitative Approaches -- 3. Algebraic Systems Theory -- 4. Restricted Notion of a System -- Appendix III. Open Systems and Goal-Seeking Systems -- 1. Open Systems -- 2. Goal-Seeking Systems -- Appendix IV. Basic Notions in Category Theory -- Index.

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;<BR id="CRLF">methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and<BR id="CRLF">methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.<BR id="CRLF"><BR id="CRLF">As a result, the book represents a blend of new methods in general computational analysis, <BR id="CRLF">and specific, but also generic, techniques for study of systems theory ant its particular<BR id="CRLF">branches, such as optimal filtering and information compression.

Description based on print version record.